Tuning, timbre, spectrum, scale
by William A. Sethares · first published 1998
82% recommend18% neutral
Why HN recommends it
Explains how timbre and the harmonic spectrum shape which intervals and scales sound consonant, with engineering-minded depth; suits engineers and musicians curious about the physics behind tuning and music theory.
Summarised by Claude from recommending comments
The only things truly universal in music are those that are based on biological and/or perceptual facts. Tuning Timbre Spectrum Scale focuses on perceptions of consonance and dissonance, which are defined in the Harvard Dictionary of Music: "Consonance is used to describe the agreeable effect produced by certain intervals as against the disagreeable effect produced others. Consonance and dissonance are the very foundation of harmonic music... consonance represents the element of smoothness and repose, while dissonance represents the no less important elements of roughness and irregularity.^ T
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…reference the most interesting work done in this area. The ones I've found most convincing are: - Dmitri Tymoczko's Geometry of Music: http://dmitri.tymoczko.com/geometry-of-music.html - Bill Sethares's Tuning Timbre Spectrum Scale approach: http://sethares.engr.wisc.edu/ttss.html - Andrew Duncan's Combinatorial Music Theory: http://andrewduncan.net/cmt/ Some of this work is pretty old at this point. Granted, it's surprisingly…
on “Harmony Explained: Progress Towards a Scientific Theory of Music (2014)” ↗Yep! Many traditions got their notes the same way Western music did. The Tuning, Timbre, Spectrum, Scale book does a great job illuminating this.
on “Music theory for nerds” ↗…Music: a Mathematical Offering, Dave Benson. Explains the mathematical theory of how to compute the timbre of an instrument given its shape. Also how the timbre of the instruments determines harmony. * Tuning, timbre, spectrum, scale, William Sethares. A deep exploration of the relationship between timbre and harmony. It starts by exhibiting a (synthetic) instrument whose octaves are dissonant, and the music that you can do with…
on “The Ghost in the MP3 (2014)” ↗…sharps, feels rather arbitrary today. Unfortunately, there are not a lot of great resource that tell this full story. The two books I found most enlightening in piecing together the "real story" are: - Tuning, Timbre, Spectrum, Scale: https://www.amazon.com/Tuning-Timbre-Spectrum-William-Sethar... - A Geometry of Music: https://www.amazon.com/Geometry-Music-Counterpoint-Extended-...
on “Music theory for nerds” ↗…differently (e.g., a tuned circular drum; or you can make a synthesized instrument that does anything you like) and different chords will sound good on them. For much more on this, see William Sethares's book "Tuning, Timbre, Spectrum, Scale" and his web pages at http://eceserv0.ece.wisc.edu/~sethares/ttss.html where you can find, e.g., some music in unorthodox scales performed on (synthetic) instruments designed to make the harmony sound…
on “Mathematical explanation of music and white/black notes in a piano” ↗I read that several years ago, when it first came out, and it blew my mind. I also highly recommend Tuning, Timbre, Spectrum, Scale by William Sethares [1]. It's a different approach to deriving our familiar harmonic structures, with a greater emphasis on consonance within a given timbre than voice leading. [1] https://www.amazon.com/Tuning-Timbre-Spectrum-William-Sethar...
on “Harmony Explained: Progress Towards a Scientific Theory of Music” ↗I'm not the parent, but I think they are referring to William Sethares' book "Tuning, Timbre, Spectrum, Scale": https://www.springer.com/gp/book/9781852337971 It's a fascinating take on how those concepts relate to each other. You can find some of the papers that were synthesized into that book on his web page:…
on “The Fine Art of Combining Harmonics” ↗…clearly, engagingly, and with an appropriate skepticism for received wisdom. Here's his discussion of some more political criticisms of music theory: https://youtu.be/Kr3quGh7pJA I recommend Sethares' _Tuning, Timbre, Spectrum, Scale_ to anyone interested in the underpinnings of why some notes sound good together and others don't. [2]https://www.researchgate.net/publication/287019948_Tuning_ti...
on “Ask HN: Tools to Learn Music Theory?” ↗The books Tuning, Timbre, Spectrum, Scale [1] and Rhythm and Transforms [2] by Sethares have a lot of detail about the perception of higher level phenomena like pitch and rhythm. Plus he's an electrical engineer, so you get some code out of the…
on “How the Ear Works: Nature's solutions for listening (1997)” ↗Highly recommend the book “Tuning Timbre Spectrum Scale” for engineers interested in music theory https://sethares.engr.wisc.edu/ttss.html
on “Everything we can't describe in music” ↗Have you read Sethares' Tuning Timbre Spectrum Scale book or the shorter paper? It gets right in on the topic of the interrelationship between timbre and dissonance. As you say, the timbres of the instruments are very important to how dissonance is or isn't…
on “Harmony Explained: Progress Towards a Scientific Theory of Music (2012)” ↗…is pretty bad. There are so many little things wrong with it that if I started trying to address them all I'd be here forever. Anybody interested in this stuff would be better off with something like Tuning Timbre Spectrum Scale (https://sethares.engr.wisc.edu/ttss.html) or Music a Mathematical Offering (https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus...)
on “Harmony Explained: Progress Towards a Scientific Theory of Music (2012)” ↗"Three Ears" by William Sethares is an example piece for his book "Tuning Timbre Spectrum Scale" that demonstrates this: http://sethares.engr.wisc.edu/mp3s/Three_Ears.mp3 "As each new note sounds, its pitch (and that of all currently sounding notes) is adjusted microtonally (based on its spectrum)…
on “The Saddest Thing I Know about the Integers” ↗He has a book about it - Tuning, Timbre, Spectrum, Scale. Unfortunately, I don't know of anyone who has tried to reproduce his results and make them more easily approachable for broader use, at least not thus far.
on “The Case for Challenging Music” ↗